Calculation of solubility product, aluminium oxide (Salze-75) The solubility product of an aluminium oxide solution is 1·10-33 mol5/L5. According to the solubility product, it is very poorly soluble in water. Calculate exactly how much gram would dissolve in a liter of water.

  Exercise: Salze-75    

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The solubility product of an aluminium oxide solution is 1·10^-33 mol⁵/L⁵. According to the solubility product, it is very poorly soluble in water. Calculate exactly how much gram would dissolve in a liter of water.

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Solution:

Note The participating ions are Al³⁺ or O^2-

1. Al₂O₃ ⇄ 2·Al³⁺ + 3·O^2-
2. L_p = c²(Al³⁺)·c³(O^2-)
3. For the number of particles, note '=':
       c(Al₂O₃) = ½·c(Al³⁺) = ⅓·c(O^2-)      
       c(Al³⁺) = 2·c(Al₂O₃)       and:
       c(O^2-) = 3·c(Al₂O₃)       thus holds:
4. L_p = [2·c(Al₂O₃)]² · [3·c(Al₂O₃)]³
5. L_p = 4·27·c²(Al₂O₃)·c³(Al₂O₃) = 108·c⁵(Al₂O₃)
6. c(Al₂O₃) = 5te roots from (L_p/108) = 5te roots from (1·10^-33/108) = 9.8·10^-8 mol/l
7. From c=n/V=m/M/V follows …
       m = c·V·M = 9.8·10^-8 mol/L · 1.0 L · 102 g/mol = 9.9·10^-6 g = 1·10^-5 g

Es solving itself thus maximum approx. 0.00001 grams aluminium oxide in a litres water. The salt is really very poorly soluble in water.

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